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We study a three dimensional Lotka–Volterra systems. In the paper Bobieński and Żołądek (J Ergod Theory Dyn Syst 25:759–791, 2005) four cases of center (i.e. an invariant surface supporting a center) were found. In this paper, we study a codimension 2 component LV  Hopf  and its versal deformation. We prove that at most one invariant torus may appear. This invariant torus corresponds to the limit cycle bifurcating in the amplitude system.

Invariant Torus in 3D Lotka–Volterra Systems Appearing After Perturbation of Hopf Center